1. The characteristic impedance of a transmission line is given by the equation:

zo = R + jwL W G + jwC


A transmission line-under-test has the following primary constants:


L = 100 x 10-9 Henries per metre

R = 4 x 10-3 Ohms per metre

G = 1 x 10-7 Siemens per metre

C = 20 x 10^-2 Farads per metre


Calculate the magnitude of the characteristic impedance with an 8 kHz line
signal frequency. Comment on the result and mention any reasonable
assumptions made in your solution.

Ω

1. Am I correct to square root this equation?
2. Now I have completed the equation, should I have broken it down into stages to reach a resolution?

 

Why would you want to take the square root of the right hand part of the equation?
That would alter the dimensions and make the equation invalid.

\(Z_0 = \sqrt{\frac{(j\omega L+ R)}{(j\omega C + G)}}\)

http://www.amanogawa.com/archive/docs/C-tutorial.pdf

 

I am not sure why I would want to square root it at all, that is why I asked?

On your picture it shows the how equation square rooted? I assumed that's what I had to do here? Are you suggesting from your notes that you supplied (many thanks) that I follow the whole process?

 

You cannot just take the square root of one side of an equation willy nilly.

Here is a simple example:

Distance travelled = velocity/time

If I were to square the right-hand side of the equation for whatever whim, that would result in (velocity/time) squared which would give area as the result. Obviously, distance cannot be equal to area.

The dimensions of \((j\omega L + R)\) are Ohms.
The dimensions of \(\frac{1}{(j\omega C + G)\) are Ohms.

Hence when we take the product the result is in \( Ohms^2\).

Taking the square root makes the equation dimensionally balanced.

 

So I square root the answer?

 

If this is your equation, no, you cannot take the square root.

zo = R + jwL W G + jwC

If you examine this equation you will notice that this equation is dimensionally unbalanced and therefore incorrect.

The dimensions of jωC are not Ohms.

I suggest you review the notes in the link provided and find the proper equation.

The lesson here is: check the dimensions of both sides of the equation.